On measuring grounding and generalizing grounding problems

Abstract: The symbol grounding problem asks how tokens like cat can be about cats, as opposed to mere shapes manipulated in a calculus. We recast grounding from a binary judgment into an audit across desiderata, each indexed by an evaluation tuple (context, meaning type, threat model, reference distribution): authenticity (mechanisms reside inside the agent and, for strong claims, were acquired through learning or evolution); preservation (atomic meanings remain intact); faithfulness, both correlational (realized meanings match intended ones) and etiological (internal mechanisms causally contribute to success); robustness (graceful degradation under declared perturbations); compositionality (the whole is built systematically from the parts). We apply this framework to four grounding modes (symbolic; referential; vectorial; relational) and three case studies: model-theoretic semantics achieves exact composition but lacks etiological warrant; LLMs show correlational fit and local robustness for linguistic tasks, yet lack selection-for-success on world tasks without grounded interaction; human language meets the desiderata under strong authenticity through evolutionary and developmental acquisition. By operationalizing a philosophical inquiry about representation, we equip philosophers of science, computer scientists, linguists, and mathematicians with a common language and technical framework for systematic investigation of grounding and meaning.